Golden Ratio Anyons: Topological Error Correction with Fibonacci Quantum Dimensions — E8 Intelligence Research

FINDING: Fibonacci anyons (quantum dimension φ) provide a topological error-correction code whose logical error rate scales with code distance, with thresholds tied to the golden ratio's algebraic structure. | MATH: Fibonacci anyon fusion rules: φ × φ = 1 + φ (where φ = (1+√5)/2 ≈ 1.618); quantum dimension d = φ satisfies d² = d + 1. Error suppression: logical error rate P_L ∝ (P_threshold/P_physical)^(⌈d/2⌉) for code distance d. Turaev-Viro code threshold: ~0.1–0.15% (Schotte et al., QIP2021). Surface code (non-Fibonacci) threshold: ~1% (Satzinger et al., Google). | CONNECTION: The Fibonacci anyon's quantum dimension is *exactly* the golden ratio φ. The fusion algebra is the golden-ratio quadratic field ℚ(√5). The Turaev-Viro invariant is a state-sum over triangulations — a lattice structure whose partition function encodes 3D topological order, with the golden ratio appearing as the normalization factor. The code distance scaling mirrors the Fibonacci sequence: code distance d grows Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com